Strength Of Brittle Materials Research Articles

Effect of rod-like and flake-like additive particles on fracture mechanisms and mechanical anisotropy of sintered Nd-Fe-B magnets

The particles of different shapes, multi-walled carbon nanotubes (CNTs) and graphene nanosheets (GNs), were used to modulate the mechanical properties and anisotropy of the magnets. It is found that the rod-shaped CNTs can increase the bending strength ratio of the c and a axes of the magnet from 1.114 to 1.254, while flake-like GNs decrease it from 1.114 to 0.989. In-depth analysis indicates that the mechanical anisotropy of the magnet is greatly influenced by the distribution and thickness of the rare earth phase (RE phase), with the thicker RE phase demonstrating greater capability of blunting at the crack tip. Using the finite element method, it is found that the strength of brittle material can be enhanced by the additive particles owing to the inhibition of crack initiation and stress conduction, as well as the deflection of the crack. The flake-like GNs weaken the mechanical anisotropy of magnets by varying the distribution of RE phase and form a shell encompassing the main phase. Nonetheless, the alignment of CNTs occurring in the process of magnetic orientation process can significantly increase the mechanical anisotropy of the magnet. In particular, when loaded in the parallel c axis (c∥) direction, the cracks need to penetrate the main phase due to the strong frictional interlocking between CNTs and the main phase grains, in which case the bending strength will be significantly increased. By contrast, when loaded in the vertical c axis (c⊥) direction, the cracks can bypass the rod-like particles and change directions of propagation. As such, the increase in bending strength is smaller than that in loading along with the c∥ direction.

Nano-samples give higher brittle strength by the Griffith energy principle

The purpose of this paper is to show that brittle test samples give a huge size effect that can take several different forms depending on the sample geometry, crack position and mode of force application. Sometimes crack equilibrium force depends on sample dimension d or d1/2 and sometimes the force is independent of area, for example in peel or lap joint cracking. This big size effect arises from the potential energy term in the conservation theory, not considered by Griffith but dominating certain cracks. These examples illustrate the fact that strength of a brittle material containing a crack is an unsatisfactory concept because the cracks absorb surface energy driven by volume energy terms or by potential energy terms or a mixture of the two, leading to a disconnection between applied cracking force and sample cross-section area. The flaw statistics argument mentioned by Griffith is unnecessary, though strength can be affected in certain circumstances by the presence of random flaws. An unusually large size effect is shown experimentally for thermal shock of ceramic tubes, in which the cracking force increases as the cube of diameter goes down. This thermal shock resistance of fine tubes has proved important for application of ceramic fuel cells but cannot be explained by fracture mechanics theory at present. The conclusion is that experimental results show the Griffith energy criterion for cracking is correct whereas the Galilean stress criterion fails. The concept 'strength of brittle materials' is therefore untenable for most crack testing geometries. This article is part of the theme issue 'Nanocracks in nature and industry'.

Structural-Temporal Peculiarities of Dynamic Deformation of Layered Materials.

The temporal nature of static and dynamic deformation of fibre metal laminates is discussed here. The aim of the study is to verify the proposed innovate model using layered composites. The modified relaxation model is based on the earlier formulated plasticity relaxation model for homogeneous materials. The proposed relaxation model makes it possible to describe the deformation of the layered composites from elastic to irreversible deformation, finalised by the failure moment. The developed approach allows us to consider the effects of the transition from static to dynamic loading. This means that the model-calculated dynamic limiting characteristics of the metal and the strength of brittle materials will have a determining character, depending on the loading history. The verification of the model using a glass fibre reinforced aluminium composite, glass fibre reinforced titanium composite, carbon fibre reinforced aluminium composite, and Kevlar fibre reinforced aluminium composite with different thickness ratios between metal and polymer layers is given. It is shown that the theoretical deformation curves of the metal composites at the various strain rates, finalised by brittle fracture of the polymer layers or continued irreversible deformation of remaining unbroken metal layers with destroyed polymer (fibre/epoxy) layers, are predicted. Based on the same structural−temporal parameters for five (Ti/GFRP (0/90)/Ti/GFRP(90/0)/Ti) and three (Ti/GFRP(0/90/90/0)/Ti) layers glass fibre reinforced titanium composites and the polymer layers, one-stage and two-stage stress drops during the irreversible deformation of the composite under static and dynamic loading are simulated. The change of the multi-stage fracture of the composite from static to dynamic loading and the fracture characteristic times of the polymer (100 s and 15,400 s) and the metal (8.4 ms) are correlated. Continued plastic deformation of the composite after fracture of the polymer layers is related with different values of the characteristic relaxation times of the polymer (fibre/epoxy) and the metal layers.

A cracking approach to inventing new tough materials: fracture stranger than friction.

A cracking approach to inventing new tough materials: fracture stranger than friction.

Brittle material strength and fracture toughness estimation from four-point bending test

The failure stress under four-point bending cannot be considered as an intrinsic material property because of the well-known size effect of increasing maximum flexural stress with decreasing specimen size. In this work, four-point bending tests are analyzed with the coupled criterion for different sample sizes. The maximum flexural stress only tends towards the material tensile strength provided the specimen height is large enough as compared to the material characteristic length. In that case, failure is mainly driven by a stress criterion. Failure of smaller specimens is driven both by energy and stress conditions, thus depending on the material tensile strength and fracture toughness. Regardless of the material mechanical properties, we show that the variation of the ratio of maximum flexural stress to strength as a function of the ratio of specimen height to material characteristic length follows a master curve, for which we propose an analytical expression. Based on this relation, we propose a procedure for the post-processing of four-point bending tests that allows determining both the material tensile strength and fracture toughness. The procedure is illustrated based on four-point bending experiments on three gypsum at different porosity fractions.

A distribution-free tracking interval for model selection: application in the strength of brittle materials

In the literature of model selection, Vuong’s test and Akaike information criterion aim to find the best statistical model. Both of them are related to the expectation of the log-likelihood function of the rival models, but they are not sensitive to the small difference between rival models. The goal of this study is to develop a simple model selection approach which does not assume a true distribution for data. We have introduced a nonparametric tracking interval in the context of model selection. We have shown that this interval is compatibale with the known Vuong’s test results, but here we let the magnitude of the data enhance the performance of statistical inference. Simulation study provide this method works well. It is shown that this interval has acceptable results for classical densities, autoregressive models and finite mixture models. This tracking interval is illustrated on a real data. The strength(mechanics) of brittle materials in various applications is characterized by Weibull distribution. These kind of data are usually skewed and platykurtic or leptokurtic. Thus, their median is more precise than their mean. Using the proposed interval, it is shown that, sometimes the Gamma and Log-normal distributions are suitable alternative to Weibull distribution.

Multiple Pseudo-Plastic Appearance of the Dynamic Fracture in Quasi-Brittle Materials.

Understanding and simulating the dynamic response of quasi-brittle materials still remains as one of the most challenging issues in structural engineering. This paper presents the damage propagation material model (DAMP) developed in order to obtain reliable results for use in structural engineering practice. A brief overview focuses on the differences between fracture mechanics studies, and engineering material modelling is presented to highlight possible guideline improvements. An experimental dynamic test performed on ultra-high-performance concrete specimens was used to obtain evidence of the physical behaviour of brittle materials with respect to specimen size variations and, consequently, to verify the reliability of the material equations proposed. Two widely used material models (RHT and M72R3), as representatives of the classical brittle material models for structural purposes, and the proposed material model are compared. Here, we show how: (i) the multiple structural strength of brittle materials arises from the damage propagation process, (ii) there is no contradiction between fracture mechanics and the engineering approach once the velocity of damage propagation is chosen as fundamental material property and (iii) classical dynamic material models are intrinsically not objective with related loss of predictive capability. Finally, the original material model equation and the experimental strategy, dedicated to its extended verification, will be shown in order to increase the design predictiveness in the dynamic range considering structure and specimen size variations. The dynamic stress increasing factor (DIF), experimentally observed and widely recognised in literature as a fundamental concept for quasi-brittle material modelling, has been reviewed and decomposed in its geometrical and material dependencies. The new material model defines its DIF starting from the physical quantities of the damage propagation velocity applied to the test case boundary conditions. The resultant material model predictiveness results improved greatly, demonstrating its ability to model several dynamic events considering size and dynamic load variations with a unique material property set without showing contradictions between numerical and experimental approaches.

Determination of Tensile Strength by Modified Brazilian Disc Method for Nuclear Graphite

The Brazilian disc test has been used widely to measure the tensile strength of brittle materials, such as rock and ceramic. However, the Brazilian disc method developed for rock has not been applicable for nuclear graphite due to the large ratio of tensile to compressive strength in the material. According to the results of stress analysis and Griffith’s strength criteria, the graphite compressive stress near the contact area must be decreased for the Brazilian tensile strength method. In this paper, the Brazilian disc test has been modified by using a newly developed anvil with a V-shaped cavity. According to finite element analysis, the stress concentration around the contact area between graphite samples and anvils was significantly reduced by the new design of anvils. The design has been proved to be effective by comparing with the direct methods. The method also has been proved to be valid for different samples sizes considered in this study, which indicates that it has a wide applicability.

Energy and strength in brittle materials

A study concerning the strength of brittle materials is presented in this paper. The failure behavior was investigated examining the plane of the crack after the failure and comparing the results obtained with those deriving from the fracture mechanics theory. Although the proposed methods are valid in general for brittle materials, the experiment was performed on glass because the results are more significant for this. Glass elements of various sizes and different edge finishes were subjected to bending tests until collapsing. The bending results were studied in terms of failure load and energy dissipation, and the fracture surfaces were examined by means of microscopic analysis, in which the depth of the flaw and the mirror radius of the fracture were measured and the strength was calculated. These results agreed with those obtained from the fracture mechanics analysis.

Localized Structural Instability and Dynamic Strength of Brittle Materials

Localized Structural Instability and Dynamic Strength of Brittle Materials

Localized Structural Instability and Dynamic Strength of Brittle Materials

Four brittle materials are subjected to shock tests: gabbrodiabase, two modifications of cast iron, fused quartz, and beryllium. An interferometer is used to locally probe a free surface in order to calculate its velocity, thereby determining the criterion of the initial stage of brittle fracture of all materials tested—the formation of horizontal steps at the forefront of a compression pulse, which indicate the presence of local sources of fracture of the material. It is determined that the brittle material resists the shock compression as long as it has the reversible transfer of momentum and energy of the processes occurring at meso- and macrolevels.

Kinetic approach to the development of computational dynamic models for brittle solids

The paper presents an approach to developing the mathematical formalism of the discrete element method to numerically study the inelastic behavior and fracture of brittle materials under dynamic loading. The approach adopts the basic principles of the kinetic theory of strength which postulate the finite time of nucleation of discontinuities and relaxation of local stresses in the material. A general methodology is proposed for constructing dynamic (kinetic) models of the mechanical behavior of a discrete element based on quasi-static models and using three dynamic material parameters (time parameters). The physical meaning of these parameters is discussed, and a method is proposed for estimating the magnitude of the parameters for a considered material using standard experimental data on its mechanical characteristics. The approach is verified by a dynamic formulation of two-parameter models of inelasticity and strength of brittle materials within the method of simply deformable discrete elements. The proposed way to the dynamic generalization of conventional quasi-static mechanical models is applicable to various Lagrangian numerical methods and makes it possible to numerically study the dynamic behavior features and to predict the mechanical characteristics of brittle materials at different strain rates (up to strain rates 103 s−1) and different types of stress state.

Modeling for Distribution of Compressive Stress from Loading Platens in Diametrical Compression Test

Diametrical Compression test is one of indirect tests to investigate the tensile strength of brittle materials. This test is spread because of easiness to perform. However, results from this test are not stable. Traditionally, calculations for this test are performed under a pair of opposite concentrated loading on the diameter of specimen. However, contact areas appear just before fracture of specimen in the fact and the stress distribution from loading platens is not obvious. It seems be one of reasons why the result from this test is not stable. In this study, the attempt to establish the modeling for distribution on loading platens in the diametrical compression test is shown. The aim of this modeling is to calculate stresses and displacement of specimen using complex stress function by Lekhnitskii. Therefore, this model is expanded in Fourier expansion. Accuracy of calculation using Fourier expansion depends on the number of terms. Therefore, the influence of contact area and number of terms to accuracy is also discussed.

Stress Distribution in Specimen for Diametrical Compression Test under Some Boundary Conditions

Diametrical Compression test is one of indirect tests to investigate the tensile strength of brittle materials. This test is spread because of easiness to perform. However, results from this test are not stable. Traditionally, calculations for diametrical compression test are performed under a pair of opposite concentrated load on the diameter of specimen. In the fact, contact areas are appears just before fracture of specimen and the stress distribution from loading platens is not obvious. It seems one of reasons why the result from this test is not stable. Several stress distributions between contact area and specimen have been proposed and stresses and strains have been calculated as theoretical results or analytical result in previous studies. In this study, the stress distribution that consists of uniform loading and cosine curve shaped loading is proposed and used for theoretical solution. Furthermore, results from this study are compared with results from previous studies.

Strength of brittle materials in moderately corrosive environments

AbstractThe strengths of four brittle materials―cordierite glass ceramic, fused silica, silicon, and polycrystalline alumina were measured after exposure to weakly corrosive water and moderately corrosive buffered HF (BHF) solution. Exposure to water did not alter the strengths in subsequent inert strength tests and decreased the strengths in reactive strength tests. Exposure to BHF increased the strengths in both tests, but only after an incubation exposure time. Prior to the incubation time, the BHF had the same effect as water, suggesting that the bond rupture kinetics were unaffected. Examination of strength‐controlling indentation flaws after the incubation time showed clear corrosive effects on the flaw geometry indicative of reductions in the indentation residual stress fields. The implication is that moderately corrosive environments increase the strength or lifetime of a brittle component by reducing the crack driving force via flaw alteration and do not, as perhaps expected, decrease the strength or lifetime through enhanced chemical reactivity.

A modified Kolsky method for determining the shear strength of brittle materials

A new modification of the Kolsky method is proposed, according to which a loaded sample is arranged in an obliquely cut tube casing. Using this configuration, it is possible to determine the shear stress of low-plasticity materials.

Flexural vs. tensile strength in brittle materials

The tests leading to the determination of the strength of brittle materials show a very wide scattering and a noticeable difference between flexural and tensile strengths. The corresponding statistics are usually described by the Weibull law, which only partly explained the observed difference. From a theoretical point of view, the coupled criterion reaches the same conclusion, the flexural strength is higher than the tensile one. It is shown that these two approaches complement to give a satisfying explanation of the difference between the flexural and tensile strengths. Moreover, according to the coupled criterion, the tensile strength appears to be the only material parameter.

Integrated assessment procedure for determining the fracture strength of glass components in CSP systems

The structural integrity and reliability of glass components are key issues for concentrated solar power (CSP) systems. For example, the glass windows in a solar furnace may suffer catastrophic fracture due to thermal and structural loadings, including reaction chamber pressure cycling. Predicting design strength provides the basis for which the optical components and mounting assembly can be designed so that failure does not occur over the operational lifetime of a given CSP system. The fracture strength of brittle materials is dependent on the size and distribution of cracks or surface flaws. Due to the inherent brittleness of glass resulting in catastrophic failure, conservative design approaches are currently used for the development of optical components made of glass, which generally neglect the specific glass composition as well as subcritical crack growth, surface area under stress, and nature of the load – either static or cyclic – phenomena. In this paper, several methods to characterize the strength of glass are discussed to aid engineers in predicting a design strength for a given surface finish, glass type, and environment. Based on the Weibull statistical approach and experimental data available on testing silica glass rod specimens, a theoretical model is developed for estimating their fracture strength under typical loading conditions. Then, an integrated assessment procedure for structural glass elements is further developed based on fracture mechanics and the theory of probability, which is based on the probabilistic modelling of the complex behaviour of glass fracture but avoids the complexity for calculation in applications. As an example, the design strength of a glass window suitable for a solar furnace reaction chamber is highlighted.

A Measurement Method of Tensile Strength for Irregular Small Stones

This article studied the drilling loading method for the tensile strength of irregular small-stone, designed the measuring devices, and addressed the measurement problems of irregular small-stone tensile strength. Based on static equilibrium theory, it analyzed the distribution rule of tensile stress in dangerous section, and established the mechanics model of drilling loading method. In considering the impact rules of characteristic destruction size and round-hole size on the hole-edge stress concentration, on this basis it established the theoretical formulas of measuring the tensile strength of brittle materials. It practically measured the failure load of small drilling bluestone, introduced the failure load into the theoretical measurement formula of brittle material tensile strength, and then obtained the tensile strength of stones, while it measured the tensile strength of non-porous strip specimen. The tensile strength of irregular stones measured by the drilling loading method is basically consistent with the tensile strength obtained from the tensile test of non-porous strip specimen, and therefore the drilling loading method is able to reasonably measure the tensile strength of small stones.

Estimation and inference in sets of Weibull samples

Menon’s method of estimation of the Weibull parameters is extended to the analysis of multiple samples of a common size. A methodology is developed for testing the equality of shape parameters among the populations from which the samples are drawn. When the shape parameters are judged to be equal, point and interval estimates of the common shape parameter are constructed. An analysis of variance approach is shown to be valid for testing the equality of scale parameters when a common shape parameter is hypothesized. A post hoc multiple comparison test is developed for assessing which scale parameters differ. Confidence intervals on a percentile may be set for any of the sample populations using the estimated common shape parameter. Tables of the percentage points of the distributions needed for testing hypotheses and constructing interval estimates were obtained by Monte Carlo sampling and are given for a useful range of sample sizes and number of samples. The result is a comprehensive, easily computed, method of analyzing uncensored sets of Weibull data such as occurs when the flexural strength of brittle materials is observed under different conditions of formulation, finishing or test environment. An example analysis of data of this type is included.